Rewrite the equation by completing the square. $x^{2} + x -72 = 0$ $(x + $
Solution: $\begin{aligned} x^2 + x -72&=0 \\\\ x^2 + x&=72 \end{aligned}$ Now we want to complete $x^2 +x$ into a perfect square. To do that, we should add $\left(\dfrac{{+1}}{2}\right)^2={\dfrac{1}{4}}$ to it: $x^2{+}x + {\dfrac{1}{4}}=\left(x +\dfrac{1}{2} \right)^2$ $\begin{aligned} x^2 + x&=72 \\\\ x^2 + x + {\dfrac{1}{4}}&=72 + {\dfrac{1}{4}} \\\\ \left(x +\dfrac{1}{2} \right)^2&=\dfrac{289}{4} \end{aligned}$ In conclusion, the equation after completing the square is written as: $\left(x +\dfrac{1}{2} \right)^2=\dfrac{289}{4}$